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th
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s
:
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iv
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ar
ch
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u
r
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Mo
d
ellin
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R
OV
Su
b
m
ar
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T
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rticle
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r th
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CC B
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.
C
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s
p
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A
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:
Mo
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a
m
ed
Mo
u
s
tan
ir
Dep
ar
t
m
en
t o
f
E
lectr
ical
E
n
g
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in
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Hass
a
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I
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Un
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s
it
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Natio
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Hi
g
h
Sch
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o
l o
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icit
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Me
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s
“
E
NSE
M”
,
C
asab
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Mo
r
o
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m
ail:
m
o
h
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m
ed
.
m
o
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s
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@
en
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m
.
ac
.
m
a
1.
I
NT
RO
D
UCT
I
O
N
R
e
m
o
tel
y
o
p
er
ated
v
eh
icles
(
R
OVs
)
,
lik
e
all
u
n
d
er
w
ater
v
eh
icles
[
1
]
,
h
av
e
g
r
o
w
n
in
i
m
p
o
r
ta
n
ce
o
v
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s
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o
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ip
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le
[
2
]
,
b
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au
s
e
th
e
u
n
d
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w
a
ter
en
v
ir
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n
m
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t
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if
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Ma
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ec
t
s
o
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tio
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i
s
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io
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s
[
3
]
,
in
v
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tar
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f
ield
s
s
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ch
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as
s
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Fi
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1
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w
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m
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e
r
o
b
o
t
w
it
h
r
ea
r
p
r
o
p
eller
,
r
u
d
d
er
s
,
an
d
d
iv
in
g
b
ar
s
(
E
C
A
g
r
o
u
p
)
Fig
u
r
e
2
.
A
li
s
tar
r
o
b
o
t w
ith
f
o
u
r
r
ea
r
p
r
o
p
eller
s
(
E
C
A
g
r
o
u
p
)
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
P
re
s
ent
a
t
i
o
n
T
h
e
g
en
er
al
co
n
ce
p
t
o
f
th
is
v
eh
ic
le
w
as
p
r
ese
n
ted
i
n
t
h
e
ar
ticle
[
6
]
w
h
ich
p
r
ec
ed
es
t
h
i
s
s
t
u
d
y
,
it
d
escr
ib
es
in
ad
d
itio
n
to
t
h
e
s
h
ap
e
o
f
t
h
i
s
v
e
h
icle,
t
h
e
ad
v
an
ta
g
e
s
an
d
d
is
ad
v
a
n
ta
g
es
o
f
th
i
s
ar
ch
i
tectu
r
al
s
o
lu
tio
n
.
I
n
th
e
s
a
m
e
w
a
y
,
we
w
er
e
ab
le
to
d
e
m
o
n
s
tr
ate
i
n
o
u
r
last
p
u
b
licatio
n
[
7
]
th
a
t
in
a
r
ea
l
aq
u
atic
en
v
ir
o
n
m
e
n
t,
t
h
is
R
OV
as
Fi
g
u
r
e
3
ca
n
m
o
v
e
a
n
d
ex
ec
u
te
th
e
o
r
d
er
s
r
ec
eiv
ed
.
T
h
u
s
,
as
d
em
o
n
s
tr
ated
,
th
e
m
o
s
t c
o
m
m
o
n
en
g
i
n
e
th
r
u
s
t c
o
m
b
i
n
atio
n
s
h
av
e
b
ee
n
te
s
ted
an
d
th
e
r
es
u
lti
n
g
c
u
r
v
e
s
h
a
v
e
b
ee
n
p
r
esen
ted
.
Fig
u
r
e
3
.
P
r
o
p
o
s
ed
m
o
d
el
in
p
er
s
p
ec
tiv
e
T
w
o
ap
p
r
o
ac
h
es
ar
e
p
o
s
s
ib
le
to
h
av
e
a
d
y
n
a
m
ic
m
o
d
el
[
8
]
:
o
n
e
s
tar
tin
g
f
r
o
m
t
h
e
co
n
s
er
v
atio
n
o
f
eq
u
atio
n
s
o
f
t
h
e
k
in
etic
an
d
p
o
ten
tial
en
er
g
ies
o
f
L
ag
r
a
n
g
e
-
E
u
ler
[
9
]
,
[
10
]
an
d
th
e
o
th
er
d
ev
elo
p
in
g
t
h
e
f
u
n
d
a
m
en
ta
l
eq
u
atio
n
o
f
m
ec
h
an
ic
s
n
a
m
ed
m
e
th
o
d
o
f
Ne
wto
n
-
E
u
ler
[
1
1
]
.
I
t'
s
t
h
is
last
th
at
w
as
u
s
ed
in
th
is
r
esea
r
ch
ed
w
o
r
k
s
.
T
h
e
m
o
d
eli
n
g
o
f
t
h
e
R
OV
i
n
cl
u
d
es t
h
e
k
i
n
e
m
a
tic
p
ar
t th
a
t
w
ill
f
o
c
u
s
o
n
th
e
m
o
v
e
m
e
n
t a
n
d
g
eo
m
etr
ic
r
elatio
n
s
h
ip
s
o
f
t
h
e
s
u
b
m
ar
in
e.
W
h
i
le
th
e
d
y
n
a
m
i
c
p
ar
t
w
ill
d
ea
l
w
it
h
th
e
f
o
r
ce
s
an
d
to
r
q
u
es
ac
tin
g
o
n
th
i
s
m
ac
h
i
n
e.
2.
2
.
K
inem
a
t
ic
m
o
del
T
h
e
g
lo
b
al
p
o
s
itio
n
v
ec
to
r
[1
2
]
,
[
1
3
]:
=
[
,
,
,
,
,
]
(
1
)
=
(
1
,
2
)
1
=
(
,
,
)
2
=
(
,
,
)
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1966
–
1
9
7
7
1968
I
n
th
e
s
a
m
e
w
a
y
w
e
ca
n
co
m
b
in
e
th
e
s
p
ee
d
s
:
=
(
1
,
2
)
1
=
(
,
,
)
2
=
(
,
,
)
(
3
)
I
n
co
o
r
d
in
ate
s
y
s
te
m
R
0:
1
̇
=
1
(
2
)
1
2
̇
=
2
(
2
)
2
(
4
)
w
it
h
:
1
(
2
)
=
(
−
+
+
+
−
+
−
)
(
5
)
2
(
2
)
=
[
1
0
−
0
/
/
]
(
6
)
T
h
e
R
o
ll,
P
itch
an
d
Ya
w
(
φ,
θa
n
d
ψ)
d
esig
n
ate
s
th
e
E
u
ler
's
an
g
les
(
Fi
g
u
r
e
4
)
,
w
h
ich
i
n
r
o
b
o
tics
co
r
r
esp
o
n
d
to
th
e
s
y
s
te
m
co
m
m
o
n
l
y
ca
lled
R
.
T
.
L
:
Fig
u
r
e
4
.
R
ep
r
esen
tatio
n
o
f
E
u
ler
an
g
les [
1
4
]
2.
3
.
Dy
na
m
ic
m
o
de
l
I
n
g
en
er
al,
th
e
f
o
r
ce
s
g
en
er
ated
b
y
th
e
r
o
tatio
n
o
f
th
e
ea
r
th
o
n
th
e
v
e
h
icle
ca
n
b
e
n
eg
lecte
d
co
m
p
ar
ed
to
th
e
h
y
d
r
o
d
y
n
a
m
i
c
f
o
r
ce
s
,
if
w
e
co
n
s
id
er
th
at
t
h
e
R
0
co
o
r
d
in
ate
s
y
s
te
m
is
a
Galilea
n
co
o
r
d
in
ate
s
y
s
te
m
f
ix
ed
to
t
h
e
s
u
r
f
ac
e
o
f
th
e
E
ar
t
h
.
T
h
e
d
y
n
a
m
ic
s
i
m
u
latio
n
w
il
l
b
e
in
s
p
ir
ed
b
y
th
e
w
o
r
k
o
f
Fo
s
s
e
n
[
9
].
I
n
th
i
s
r
ef
er
en
ce
,
t
h
e
f
u
n
d
a
m
e
n
tal
p
r
in
cip
le
o
f
t
h
e
d
y
n
a
m
ics
ap
p
lied
to
th
e
m
o
b
ile
g
iv
e
s
[
1
5
]:
̇
=
+
+
ℎ
+
+
(
7
)
W
h
er
e
th
e
v
ec
to
r
s
:
̇
=
[
̇
,
̇
,
̇
,
,
̇
̇
,
̇
]
: v
eh
icle
ac
ce
ler
atio
n
s
: f
o
r
ce
s
an
d
to
r
q
u
es o
f
d
r
iv
e
i
n
er
tia
an
d
C
o
r
io
lis
: f
o
r
ce
s
an
d
to
r
q
u
es i
n
d
u
ce
d
b
y
w
ei
g
h
t a
n
d
A
r
ch
i
m
ed
es
'
t
h
r
u
s
t
ℎ
: h
y
d
r
o
d
y
n
a
m
ic
f
o
r
ce
s
an
d
to
r
q
u
es
: f
o
r
ce
s
a
n
d
to
r
q
u
es p
r
o
d
u
ce
d
b
y
ac
t
u
ato
r
s
: e
x
ter
n
al
d
is
tu
r
b
an
ce
s
(
w
av
e
s
…)
2
.
3
.
1
.
I
nert
ia
a
nd
c
o
rio
lis
An
y
m
o
v
i
n
g
b
o
d
y
m
o
v
i
n
g
i
n
a
f
lu
id
w
h
o
s
e
d
en
s
ities
ar
e
clo
s
e,
ca
u
s
es
a
d
is
p
lace
m
e
n
t
o
f
a
ce
r
tain
q
u
an
tit
y
o
f
t
h
is
f
lu
id
d
u
r
in
g
it
s
m
o
v
e
m
en
t.
T
h
u
s
,
f
r
o
m
th
e
p
h
y
s
ical
p
o
in
t
o
f
v
ie
w
,
Ne
w
to
n
'
s
s
ec
o
n
d
la
w
is
n
o
lo
n
g
er
ap
p
licab
le
in
h
is
cla
s
s
i
ca
l
f
o
r
m
,
b
ec
au
s
e
ai
r
w
a
s
ad
m
itted
as
a
v
ac
u
u
m
an
d
t
h
e
m
as
s
o
f
th
e
d
is
p
lace
d
air
is
n
eg
l
ig
ib
le
co
m
p
ar
ed
to
th
e
m
as
s
o
f
th
e
s
o
lid
i
n
m
o
t
io
n
,
f
r
o
m
w
h
er
e
it
i
s
n
ec
es
s
ar
y
t
o
tak
e
i
n
to
ac
co
u
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
F
o
u
r
p
r
o
p
ellers
s
u
b
ma
r
in
e
d
r
o
n
e
mo
d
ellin
g
in
a
r
ea
l e
n
viro
n
men
t
(
Mo
h
a
med
Mo
u
s
ta
n
ir
)
1969
th
is
d
is
p
lace
d
m
a
s
s
o
f
f
lu
id
[
1
6
].
C
o
n
s
eq
u
e
n
tl
y
,
t
h
e
b
alan
ce
o
f
th
e
f
o
r
ce
s
d
u
e
to
t
h
e
i
n
er
tia
an
d
to
th
is
ad
d
ed
m
as
s
o
f
w
ater
m
u
s
t b
e
w
r
itte
n
in
th
e
f
o
r
m
:
∑
=
(
+
)
.
(
8
)
As
a
r
esu
lt,
r
elatio
n
(
8
)
w
h
ic
h
co
n
ce
r
n
s
th
e
m
as
s
m
atr
i
x
,
is
s
ee
n
to
b
e
d
ev
elo
p
ed
.
T
h
e
in
er
tia
m
atr
i
x
o
f
th
e
f
l
u
id
is
p
o
s
iti
v
e
an
d
s
y
m
m
etr
ica
l.
T
h
e
u
n
d
er
w
ater
v
e
h
ic
le
h
a
s
t
w
o
p
lan
es
o
f
s
y
m
m
etr
y
,
o
n
e
w
i
t
h
r
esp
ec
t to
th
e
p
la
n
e
(
x
z)
a
n
d
a
n
o
th
er
w
i
th
r
e
s
p
ec
t to
th
e
p
lan
e
(
x
y
)
a
n
d
s
i
n
ce
it
h
a
s
a
to
r
p
ed
o
s
h
ap
e,
s
o
w
e
ca
n
s
i
m
p
li
f
y
th
e
s
y
m
m
etr
ie
s
an
d
t
h
e
m
atr
i
x
ca
n
tak
e
t
h
e
f
o
llo
w
i
n
g
f
o
r
m
[
1
7
]:
=
−
[
̇
0
0
0
0
0
0
̇
0
0
0
0
0
0
̇
0
0
0
0
0
0
̇
0
0
0
0
0
0
̇
0
0
0
0
0
0
̇
]
(
9
)
Fo
r
o
u
r
R
OV:
̇
=
0
,
1
2
.
86
̇
=
2
88
.
84
̇
=
2
88
.
84
̇
=
0
0
̇
=
2
3
12
+
3
15
10
.
66
̇
=
2
3
12
+
3
15
10
.
66
L
i
k
e
w
is
e,
f
o
r
th
e
m
atr
ix
o
f
i
n
er
tia
an
d
as
th
e
ce
n
ter
o
f
th
e
r
ef
er
en
ce
,
R
v
co
in
cid
es
w
it
h
th
e
ce
n
ter
o
f
g
r
av
it
y
a
n
d
tak
i
n
g
i
n
to
ac
co
u
n
t th
e
s
y
m
m
e
tr
ies
w
e
ca
n
s
i
m
p
l
if
y
is
b
ein
g
as
[
1
7
]:
=
−
[
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
]
(
1
0
)
2.
3
.
2
.
W
eig
ht
a
nd
Arc
hi
m
ed
es' t
hrus
t
T
h
e
f
o
r
ce
s
th
at
th
e
s
u
b
m
ar
in
e
u
n
d
er
g
o
e
s
in
w
ater
ar
e
A
r
ch
i
m
ed
es
'
p
u
s
h
a
n
d
th
at
o
f
i
ts
o
wn
w
ei
g
h
t
an
d
ar
e
w
r
itte
n
:
=
.
(
1
1
)
=
.
∇
.
(
1
2
)
w
it
h
:
: v
eh
ic
le
m
a
s
s
: e
ar
th
ac
ce
ler
atio
n
:
w
ater
d
en
s
it
y
∇
:
d
is
p
lace
d
w
ater
v
o
l
u
m
e.
T
h
u
s
,
th
e
v
ec
to
r
o
f
h
y
d
r
o
s
tat
ic
f
o
r
ce
s
ca
n
b
e
w
r
it
ten
a
s
[1
6
]:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1966
–
1
9
7
7
1970
=
[
−
(
−
)
(
−
)
(
−
)
(
−
)
c
os
φ
−
(
−
)
c
os
θ
s
in
φ
−
(
−
)
c
os
φ
−
(
−
)
s
in
θ
(
−
)
c
os
φ
−
(
−
)
s
in
θ
]
(
1
3
)
w
it
h
:
B:
A
r
ch
i
m
ed
es
'
t
h
r
u
s
t (
B
u
o
y
a
n
c
y
)
i
n
N
W
: W
eig
h
t i
n
N
(
,
,
)
: th
e
p
o
s
itio
n
o
f
t
h
e
ce
n
ter
o
f
g
r
av
it
y
i
n
R
v
(
,
,
)
: th
e
p
o
s
itio
n
o
f
t
h
e
ce
n
ter
o
f
g
r
av
it
y
i
n
R
v
I
f
w
e
co
n
s
id
er
th
at
th
e
ce
n
ter
o
f
th
r
u
s
t
an
d
th
e
ce
n
ter
o
f
th
e
r
ef
er
en
ce
R
v
,
ar
e
p
lace
d
o
n
th
e
s
a
m
e
ax
is
(
Oz)
,
th
e
n
,
th
e
ce
n
ter
o
f
g
r
av
it
y
m
u
s
t
b
e
b
elo
w
th
e
ce
n
ter
o
f
th
r
u
s
t
f
o
r
th
e
s
u
b
m
ar
i
n
e
to
k
ee
p
its
p
o
s
itio
n
o
f
in
it
ial
eq
u
ilib
r
i
u
m
u
n
d
er
th
e
ef
f
ec
t o
f
th
e
r
i
g
h
tin
g
m
o
m
e
n
t (
F
ig
u
r
e
5
)
.
Fig
u
r
e
5
.
“
x
”
c
o
n
f
i
g
u
r
atio
n
i
n
r
ea
r
v
ie
w
Fro
m
w
h
er
e
=
0
,
=
0
=
−
ℎ
,
an
d
th
at
th
e
m
as
s
o
f
th
e
s
u
b
m
ar
i
n
e
is
d
is
tr
ib
u
ted
s
y
m
m
etr
icall
y
w
it
h
r
e
s
p
ec
t
t
o
th
e
t
h
r
ee
p
lan
e
s
(
)
,
(
)
(
)
,
w
e
k
n
o
w
th
at
in
R
V:
=
0
,
=
0
=
0
,
th
e
s
a
m
e
at
eq
u
ilib
r
iu
m
W
=
B
:
=
[
0
0
0
ℎ
c
os
θ
s
in
φ
ℎ
s
in
θ
0
]
(
1
4
)
2
.
3
.
3
.
H
y
dro
dy
na
m
ic
f
o
rc
es
a
nd
t
o
rques
T
h
er
e
ar
e
o
th
er
ty
p
es
o
f
h
y
d
r
o
d
y
n
a
m
ic
d
a
m
p
er
s
an
d
th
e
y
a
f
f
ec
t
p
r
i
m
ar
il
y
s
u
r
f
ac
e
s
h
ip
s
r
ath
er
th
a
n
u
n
d
er
w
at
er
v
eh
icles.
T
h
u
s
,
it
b
ec
o
m
e
s
d
if
f
ic
u
lt
to
s
ep
ar
ate
all
d
a
m
p
er
s
clo
s
el
y
,
it
is
th
e
n
n
ec
es
s
ar
y
to
e
x
p
r
ess
in
a
g
lo
b
al
w
a
y
al
l th
e
s
e
h
y
d
r
o
d
y
n
a
m
ic
d
a
m
p
i
n
g
f
o
r
ce
s
i
n
a
s
in
g
le
ter
m
w
h
ic
h
d
ep
en
d
s
o
n
t
h
e
s
p
ee
d
[
1
8
]:
ℎ
=
−
(
)
.
=
−
(
+
(
)
)
.
(
1
5
)
:
lin
ea
r
d
a
m
p
i
n
g
.
: n
o
n
-
li
n
ea
r
d
a
m
p
in
g
.
w
it
h
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
F
o
u
r
p
r
o
p
ellers
s
u
b
ma
r
in
e
d
r
o
n
e
mo
d
ellin
g
in
a
r
ea
l e
n
viro
n
men
t
(
Mo
h
a
med
Mo
u
s
ta
n
ir
)
19
71
=
[
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
]
(
1
6
)
=
[
|
|
0
0
0
0
0
0
|
|
0
0
0
0
0
0
|
|
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0
0
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|
|
0
0
0
0
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|
|
0
0
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0
0
0
|
|
]
(
1
7
)
W
h
er
e
th
e
co
ef
f
icie
n
ts
i
n
«
|
|
»
a
r
e
t
h
e
ab
s
o
lu
te
v
al
u
es o
f
t
h
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lin
ea
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s
o
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te
s
p
ee
d
s
.
T
h
e
s
u
b
m
ar
in
e
w
ill
b
e
ass
u
m
e
d
lik
e
a
cy
li
n
d
r
ical
s
h
ap
e
o
f
len
g
t
h
L
,
w
it
h
t
w
o
h
e
m
is
p
h
er
e
s
at
th
e
en
d
o
f
r
ad
iu
s
a.
A
s
t
h
e
s
u
b
m
ar
i
n
e
d
o
es n
o
t h
av
e
a
d
r
iv
e,
r
u
d
d
er
o
r
r
u
d
d
er
s
th
er
ef
o
r
e:
=
=
(
2
+
2
)
|
|
=
1
2
2
(
1
8
)
=
=
2
2
|
|
=
(
1
9
)
=
0
|
|
=
(
2
0
)
=
0
|
|
=
1
32
4
(
2
1
)
=
0
|
|
=
1
32
4
(
2
2
)
=
0
|
|
=
0
(
2
3
)
I
f
w
e
co
n
s
id
er
:
=
0
.
152
=
1
,
2
=
1020
/
3
So
,
af
ter
ca
lcu
latio
n
,
th
e
h
y
d
r
o
d
y
n
a
m
ic
co
ef
f
icie
n
ts
s
p
ec
i
f
ic
to
th
is
R
OV
w
ill b
e
g
r
o
u
p
ed
i
n
th
e
T
ab
le
1
an
d
w
e
w
i
ll b
ec
o
m
e:
T
ab
le
1
.
R
OV
s
h
y
d
r
o
d
y
n
a
m
ic
co
ef
f
icie
n
t
s
[
S.I
]
1
4
0
1
.
56
|
|
37
.
01
2
3
2
.
58
|
|
1
8
6
.
04
0
|
|
1
8
6
.
04
0
|
|
10
.
04
0
|
|
10
.
04
0
|
|
0
2
.
3
.
4
.
E
x
t
er
na
l dis
t
ur
ba
nces
E
x
ter
n
al
d
is
tu
r
b
an
ce
s
af
f
ec
ti
n
g
a
m
ar
i
n
e
v
e
h
icle
ar
e
th
e
w
i
n
d
(
o
n
ly
f
o
r
s
u
r
f
ac
e
v
e
h
icle
s
)
,
w
a
v
es
(
f
o
r
s
u
r
f
ac
e
o
r
s
u
b
s
u
r
f
ac
e
v
e
h
icle
s
)
,
an
d
cu
r
r
en
t,
b
u
t
th
e
m
o
s
t
i
m
p
o
r
tan
t
is
t
h
e
u
m
b
ilical
[
1
7
].
B
u
t
in
th
e
p
r
ese
n
ce
o
f
th
e
e
m
b
ilical,
t
h
e
d
y
n
a
m
ic
s
tu
d
y
s
h
o
u
ld
b
e
m
o
r
e
d
etailed
[
1
9
]
.
Sin
ce
it h
as
n
o
ca
b
le
f
o
r
o
u
r
R
OV
a
n
d
if
we
co
n
s
id
er
th
at
th
e
s
u
b
m
ar
in
e
w
il
l
ev
o
lv
e
i
n
ca
l
m
w
ater
s
w
it
h
o
u
t
th
e
p
r
esen
ce
o
f
w
a
v
es
o
r
cu
r
r
en
ts
,
th
ese
d
is
tu
r
b
an
ce
s
ca
n
b
e
n
e
g
lecte
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1966
–
1
9
7
7
1972
2
.
3
.
5
.
Act
ua
t
o
r
ef
f
ec
t
s
T
h
ey
d
esi
g
n
ate
g
en
er
all
y
a
n
y
p
o
w
er
s
o
u
r
ce
w
h
ich
ca
n
g
en
er
ate
a
th
r
u
s
t
ex
er
ted
o
n
t
h
e
v
eh
ic
le,
i
n
o
u
r
ca
s
e,
th
e
y
ar
e
f
o
u
r
elec
tr
ic
m
o
to
r
s
o
f
b
r
u
s
h
less
t
y
p
e
m
o
u
n
ted
in
co
n
f
i
g
u
r
atio
n
"
x
"
.
M
o
d
elin
g
t
h
e
th
r
u
s
t
o
f
a
th
r
u
s
ter
is
r
elati
v
el
y
d
elica
t
e
b
ec
au
s
e
it
d
ep
en
d
s
o
n
s
e
v
e
r
al
p
ar
am
eter
s
a
n
d
is
f
u
r
t
h
er
co
m
p
lica
ted
b
y
t
h
e
co
u
p
lin
g
o
f
s
ev
er
al
t
h
r
u
s
ter
.
B
ec
au
s
e
in
o
u
r
ca
s
e,
t
h
e
t
h
r
u
s
ts
o
f
t
h
e
f
o
u
r
t
h
r
u
s
ter
s
ar
e
p
ar
allel
to
th
e
a
x
is
Ox
.
s
ee
n
f
r
o
m
th
e
r
ea
r
,
tak
i
n
g
i
n
to
ac
co
u
n
t
th
e
co
n
f
i
g
u
r
atio
n
o
f
t
h
e
th
r
u
s
ter
s
(
Fi
g
u
r
e
5
)
.
T
h
e
v
ec
to
r
o
f
f
o
r
ce
s
an
d
to
r
q
u
es a
p
p
lied
to
th
e
v
eh
icle
b
y
t
h
e
ac
t
u
ato
r
s
is
g
en
er
all
y
d
ef
i
n
ed
as
[1
7
]:
=
(
,
,
,
Γ
,
Γ
,
Γ
)
(
2
4
)
I
n
o
u
r
ca
s
e,
s
i
n
ce
w
e
h
a
v
e
f
o
u
r
th
r
u
s
ter
s
d
ir
ec
ted
alo
n
g
th
e
Ox
ax
is
,
th
e
n
:
=
(
,
0
,
0
,
0
,
Γ
,
Γ
)
(
2
5
)
T
h
er
ef
o
r
e,
th
e
m
atr
ix
o
f
ac
tu
at
o
r
s
:
=
.
(
2
6
)
W
h
o
b
ec
o
m
es
:
=
[
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
−
−
ℎ
/
2
−
−
ℎ
/
2
+
−
ℎ
/
2
+
−
ℎ
/
2
+
−
−
+
]
.
[
1
2
3
4
]
(
2
7
)
2
.
4
.
Si
m
ula
t
io
n
2
.
4
.
1
.
Nu
m
er
ica
l r
e
s
o
lutio
n
T
h
e
MA
T
L
A
B
lan
g
u
ag
e
w
ill
b
e
u
s
ed
f
o
r
t
h
e
s
i
m
u
latio
n
o
f
th
e
m
o
v
e
m
e
n
t
o
f
t
h
i
s
R
OV,
f
o
r
th
at
we
w
il
l
i
m
p
le
m
en
t
t
h
e
p
r
o
g
r
am
i
n
th
is
la
n
g
u
a
g
e.
Si
m
i
lar
l
y
,
an
d
d
e
p
en
d
in
g
o
n
th
e
en
g
i
n
e
co
n
tr
o
ls
an
d
also
th
e
r
esp
o
n
s
e
o
f
th
e
v
e
h
icle,
t
h
e
d
escr
ib
ed
tr
a
j
ec
to
r
y
w
ill
b
e
v
is
u
alize
d
o
n
a
3
D
in
ter
f
ac
e.
T
h
e
p
ar
am
eter
s
s
p
ec
if
ic
to
th
e
R
OV
o
f
th
is
s
tu
d
y
,
a
s
w
ell
a
s
t
h
e
eq
u
atio
n
s
w
h
ich
r
e
s
u
lt
f
r
o
m
t
h
e
k
in
e
m
at
ic
,
an
d
d
y
n
a
m
ic
s
tu
d
ie
s
w
ill
b
e
in
teg
r
ated
in
to
th
e
g
lo
b
al
p
r
o
g
r
am
to
v
i
s
u
alize
th
e
v
ar
i
o
u
s
p
h
ase
s
o
f
th
e
v
eh
icle
s
i
m
u
latio
n
.
T
h
e
R
OV
eq
u
atio
n
o
f
s
tate
s
y
s
te
m
ca
n
b
e
d
ef
in
ed
as:
{
̇
(
)
=
(
)
.
(
)
̇
(
)
=
−
1
(
.
−
(
)
−
(
)
.
(
)
)
(
2
8
)
w
it
h
:
=
[
1
(
2
)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
(
2
)
]
(
29
)
an
d
:
=
−
[
̇
+
0
0
0
0
0
0
̇
+
0
0
0
0
0
0
̇
+
0
0
0
0
0
0
̇
+
0
0
0
0
0
0
̇
+
0
0
0
0
0
0
̇
+
]
(
3
0
)
So
m
e
n
u
m
er
ical
d
ata
s
p
ec
if
ic
to
th
e
R
OV:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
F
o
u
r
p
r
o
p
ellers
s
u
b
ma
r
in
e
d
r
o
n
e
mo
d
ellin
g
in
a
r
ea
l e
n
viro
n
men
t
(
Mo
h
a
med
Mo
u
s
ta
n
ir
)
1973
∆
=
∆
=
1
2
⁄
.
2
=
3
,
504
.
2
∆
=
0
,
143
.
2
1
=
60
2
=
60
(
3
1
)
=
1
,
2
=
28
,
6
=
90
ℎ
=
15
I
n
th
e
f
o
llo
w
in
g
p
ar
t,
w
e
w
i
ll
u
s
e
t
h
e
n
u
m
er
ical
r
eso
lu
t
io
n
o
f
th
e
d
i
f
f
er
e
n
tial
eq
u
a
tio
n
s
t
o
v
is
u
a
lize
th
e
d
y
n
a
m
ic
b
e
h
av
io
r
s
p
ec
i
f
i
c
to
o
u
r
s
u
b
m
ar
i
n
e
r
o
b
o
t,
o
f
w
h
ic
h
t
h
e
i
n
p
u
t
p
ar
a
m
eter
s
o
f
t
h
e
s
y
s
te
m
w
ill
b
e
o
n
l
y
t
h
e
d
if
f
er
e
n
t
p
o
w
er
co
n
f
i
g
u
r
atio
n
s
o
f
th
e
t
h
r
u
s
te
r
s
.
T
h
e
(
2
8
)
,
w
h
ic
h
g
o
v
er
n
th
e
m
o
d
el
r
esu
lti
n
g
f
r
o
m
th
e
k
in
e
m
at
ic
an
d
d
y
n
a
m
ic
s
tu
d
i
es
o
f
th
e
R
OV,
ca
n
b
e
s
o
lv
e
d
b
y
s
e
v
er
al
m
et
h
o
d
s
o
f
n
u
m
er
ical
r
eso
lu
tio
n
o
f
d
if
f
er
e
n
tial
eq
u
a
tio
n
s
,
b
u
t
in
t
h
is
c
h
ap
ter
,
w
e
h
a
v
e
o
p
ted
f
o
r
th
e
4
th
o
r
d
er
r
u
n
g
e
-
k
u
tta
(
R
K)
m
et
h
o
d
f
o
r
its
r
e
m
ar
k
ab
le
p
r
ec
is
io
n
i
n
s
o
l
v
in
g
th
i
s
t
y
p
e
o
f
eq
u
atio
n
[
2
0
]
.
2
.
4
.
2
.
I
m
ple
m
ent
a
t
io
n
T
h
is
m
et
h
o
d
is
an
e
f
f
icie
n
t
a
n
d
r
eliab
le
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
d
if
f
er
en
tial
eq
u
atio
n
s
,
a
n
d
also
ca
n
b
e
u
s
ed
i
n
a
g
e
n
er
al
w
a
y
u
s
ab
le
at
an
y
o
r
d
er
o
f
d
if
f
er
en
t
ial
eq
u
atio
n
s
.
T
o
d
o
th
is
,
it
s
u
f
f
ices
to
co
n
v
er
t
th
e
o
r
d
er
‘
n
’
o
f
th
e
eq
u
atio
n
to
b
e
s
o
l
v
ed
to
th
e
n
u
m
b
er
‘
n
’
o
f
eq
u
atio
n
s
to
b
e
s
o
lv
ed
.
Nev
er
th
eles
s
,
it
r
eq
u
ir
es
a
m
etic
u
lo
u
s
s
eq
u
en
c
in
g
f
o
r
its
ap
p
licatio
n
,
b
ec
au
s
e
it
i
n
v
o
l
v
es
f
o
u
r
ti
m
es
m
o
r
e
ca
lc
u
lati
o
n
th
a
n
th
e
E
u
ler
m
et
h
o
d
f
o
r
ex
a
m
p
le.
T
h
e
s
eq
u
en
ce
to
ap
p
l
y
t
h
i
s
m
et
h
o
d
f
o
r
s
o
lv
i
n
g
a
1
s
t
o
r
d
er
d
if
f
er
e
n
ti
al
eq
u
atio
n
w
it
h
t
h
e
4
th
o
r
d
er
R
u
n
g
e
-
Ku
t
ta
m
et
h
o
d
,
ca
n
b
e
w
r
itten
as
[2
1
]
:
(
=
0
)
=
0
1
=
(
0
,
0
)
.
2
=
(
0
+
2
,
0
+
1
2
)
.
(
3
2
)
3
=
(
0
+
2
,
0
+
2
2
)
.
4
=
(
0
+
,
0
+
3
)
.
1
=
0
+
1
6
.
(
1
+
2
2
+
2
3
+
4
)
T
h
e
d
iag
r
a
m
o
f
t
h
i
s
4
th
o
r
d
er
m
eth
o
d
ab
o
v
e
w
il
l
b
e
ap
p
lied
in
o
u
r
ca
s
e
f
o
r
th
e
s
o
lu
ti
o
n
o
f
t
h
e
eq
u
atio
n
s
.
B
u
t
w
e
m
u
s
t
f
ir
s
t
d
ec
o
m
p
o
s
e
o
u
r
eq
u
atio
n
w
h
i
ch
is
a
t
t
h
e
2
n
d
d
eg
r
ee
i
n
2
eq
u
atio
n
s
o
f
t
h
e
1
s
t
d
eg
r
ee
.
th
e
co
ef
f
icie
n
ts
o
f
R
K
w
i
ll
b
e
ca
lcu
lated
s
i
m
u
l
t
an
eo
u
s
l
y
a
n
d
alter
n
atel
y
alo
n
g
t
h
e
r
eso
lu
tio
n
p
r
o
ce
s
s
to
f
in
al
l
y
f
i
n
d
th
e
d
esire
d
v
al
u
es a
s
:
No
te:
A
ll t
h
e
s
e
co
ef
f
icie
n
ts
(
v
ec
to
r
s
an
d
m
atr
ices)
ar
e
o
r
d
er
6
.
T
h
is
alg
o
r
ith
m
w
il
l
b
e
im
p
le
m
en
ted
in
MA
T
L
A
B
in
th
e
f
o
r
m
o
f
a
p
r
o
g
r
am
w
it
h
th
e
v
a
lu
es
o
f
th
e
th
r
u
s
ts
as
in
p
u
ts
.
T
h
e
m
o
s
t
co
m
m
o
n
co
m
b
in
a
tio
n
s
o
f
th
r
u
s
t
er
s
w
ill
b
e
test
ed
to
d
eter
m
i
n
e
th
e
r
ea
ctio
n
o
f
th
e
R
OV
i
n
ea
ch
ca
s
e.
(
=
0
)
=
0
ℎ
(
=
0
)
=
ℎ
0
(3
3
)
1
=
(
0
)
.
1
=
(
ℎ
0
)
.
(
34
)
2
=
(
0
+
1
2
)
.
2
=
(
ℎ
0
+
1
2
)
.
(3
5
)
3
=
(
0
+
2
2
)
.
3
=
(
ℎ
0
+
2
2
)
.
(
3
6
)
4
=
(
0
+
3
)
.
4
=
(
ℎ
0
+
3
)
.
(3
7
)
1
=
0
+
1
6
.
(
1
+
2
2
+
2
3
+
4
)
ℎ
1
=
ℎ
0
+
.
(
1
+
2
2
+
2
3
+
4
)
(3
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t,
Vo
l.
12
,
No
.
4
,
Dec
em
b
er
2021
:
1966
–
1
9
7
7
1974
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
s
y
s
te
m
e
n
tr
ies
i
n
d
icati
n
g
th
e
v
al
u
es
o
f
t
h
e
th
r
u
s
t
s
d
ev
el
o
p
ed
b
y
th
e
t
h
r
u
s
ter
s
w
ill
b
e
g
iv
en
i
n
th
e
o
r
d
er
[
F
1
]
-
[
F
4
].
T
o
h
av
e
th
e
b
alan
ce
o
f
th
e
t
h
r
u
s
ts
,
n
o
r
m
all
y
t
h
e
y
m
u
s
t
h
av
e
t
h
e
s
a
m
e
v
al
u
e
s
.
Ho
w
e
v
er
,
as
th
e
ce
n
ter
o
f
g
r
av
it
y
o
f
th
e
v
eh
ic
l
e
is
n
o
t
o
n
th
e
ax
is
(
Ox
)
,
w
e
w
il
l
h
a
v
e
an
eq
u
ilib
r
iu
m
co
ef
f
icie
n
t
o
f
h
o
r
izo
n
tal
f
o
r
ce
s
.
So
,
th
is
co
ef
f
icien
t
w
i
ll
in
d
icate
th
e
p
r
o
p
o
r
tio
n
ality
b
et
w
ee
n
th
e
h
o
r
izo
n
tal
t
h
r
u
s
ts
an
d
h
e
is
d
ef
in
ed
as:
=
(
1
+
ℎ
)
.
2
3
(3
9
)
W
e
ca
n
s
ee
th
at
if
ℎ
=
0
w
e
h
av
e
a
p
r
o
p
o
r
tio
n
ality
o
f
=
1
w
h
en
3
=
2
.
Fo
r
ex
a
m
p
le:
3
=
22
a
n
d
2
=
14
.
T
o
g
iv
e
a
c
o
m
p
ar
ati
v
e
id
ea
b
et
w
ee
n
th
e
s
tu
d
y
i
n
an
id
ea
l
an
d
r
ea
l
en
v
ir
o
n
m
e
n
t,
w
e
w
il
l
tr
y
to
k
ee
p
th
e
s
a
m
e
co
n
f
ig
u
r
atio
n
an
d
p
r
o
p
o
r
tio
n
alit
y
s
c
h
e
m
e
s
p
r
ev
io
u
s
l
y
en
ter
ed
.
T
h
r
u
s
ter
s
h
a
v
e
p
r
o
p
o
r
tio
n
all
y
th
e
s
a
m
e
t
h
r
u
s
t
{1
8
;1
8
;2
8
;2
8
}
I
n
th
is
ca
s
e
(
Fig
u
r
e
6
)
th
e
r
o
b
o
t
k
ee
p
s
a
s
tr
aig
h
t
p
ath
.
On
l
y
t
h
e
x
p
o
s
itio
n
ch
a
n
g
e
s
,
th
e
o
th
er
f
iv
e
p
ar
am
eter
s
r
e
m
ai
n
ze
r
o
.
I
ts
s
p
ee
d
alo
n
g
th
e
O
x
ax
i
s
in
cr
ea
s
es
in
it
iall
y
,
t
h
e
n
s
tab
ili
ze
s
th
r
o
u
g
h
o
u
t
th
e
r
e
m
ain
d
er
o
f
t
h
e
s
i
m
u
latio
n
.
Fig
u
r
e
6
.
T
h
r
u
s
ter
s
h
a
v
e
p
r
o
p
o
r
tio
n
all
y
t
h
e
s
a
m
e
th
r
u
s
t
Ver
tical
th
r
u
s
ter
s
h
av
e
p
r
o
p
o
r
tio
n
all
y
t
h
e
s
a
m
e
t
h
r
u
s
t
{1
5
;1
0
;2
3
;2
8
}
W
ith
t
h
is
co
n
f
i
g
u
r
atio
n
(
F
ig
u
r
e
7
)
,
th
e
R
OV
d
escr
ib
es
a
n
ar
c
in
a
p
la
n
e
p
ar
allel
to
th
e
p
la
n
e
z
=
0
at
co
n
s
ta
n
t z
,
th
e
r
ad
iu
s
d
ep
en
d
s
o
n
t
h
e
p
o
w
er
o
f
t
h
e
t
h
r
u
s
ter
s
a
n
d
o
n
l
y
t
h
e
an
g
le
t
h
eta
v
ar
ies.
Fig
u
r
e
7
.
Ver
tical
th
r
u
s
ter
s
h
a
v
e
p
r
o
p
o
r
tio
n
ally
t
h
e
s
a
m
e
t
h
r
u
s
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
F
o
u
r
p
r
o
p
ellers
s
u
b
ma
r
in
e
d
r
o
n
e
mo
d
ellin
g
in
a
r
ea
l e
n
viro
n
men
t
(
Mo
h
a
med
Mo
u
s
ta
n
ir
)
1975
On
e
o
f
t
h
e
f
o
u
r
th
r
u
s
ter
s
i
s
p
r
o
p
o
r
tio
n
ally
d
i
f
f
er
en
t to
th
e
o
t
h
er
s
{1
8
;1
8
;2
8
;0
}
I
n
th
is
co
m
b
i
n
atio
n
(
F
ig
u
r
e
8
)
,
th
e
v
eh
icle
w
ill
d
escr
ib
e
a
s
p
ir
al
w
h
o
s
e
r
ad
iu
s
an
d
p
itch
w
i
ll
d
ep
en
d
s
o
n
th
e
s
p
ee
d
o
f
th
e
R
OV
a
n
d
th
e
d
ef
er
en
ce
o
f
th
e
p
o
w
er
o
f
t
h
is
t
h
r
u
s
ter
w
it
h
th
e
o
t
h
er
th
r
u
s
ter
s
.
Fig
u
r
e
8
.
On
e
o
f
t
h
e
f
o
u
r
t
h
r
u
s
ter
s
is
p
r
o
p
o
r
tio
n
ally
d
i
f
f
er
en
t
to
th
e
o
th
er
s
T
o
c
o
n
f
ir
m
o
u
r
r
es
u
lts
in
p
r
ac
tice,
w
e
s
tar
ted
t
h
e
r
ea
lizatio
n
p
h
ase
i
n
o
u
r
L
ab
o
r
ato
r
y
in
th
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.
T
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R
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